Reducing notch stresses: How deep rolling extends the service life of components

How can notch points in gear shafts, for example, be designed to withstand loads? And above all, how can the predictive accuracy of design guidelines be improved? A team of researchers from TU Dresden and TU Chemnitz has been working on this. The results of the research project were presented at the VDI conference "Shafts and Shaft-Hub Connections 2024" in Munich. What is interesting about this project is that Stefanie Günther and her colleagues focused specifically on how the evaluation of guidelines can be carried out taking surface and subsurface properties into account [1].

In the first semester of mechanical engineering, students learn how important it is to design shaft transitions correctly. The mechanical loads are particularly high at notch points in every component and are usually responsible for the mechanical breakage of a component. This can be illustrated particularly well with gear shafts. In a gearbox, different types of load act on the components, from tensile pressure to rotating bending to torsion; and these are usually superimposed. The mechanical loads are then particularly high at shaft heels, leading to crack initiation.

So that the designer can easily design these points, there are some guidelines for this. These frameworks are basically calculation methods for determining the probability of failure for the geometry in question. Guidelines such as the FKM guideline, DIN 743 or the new FVA guideline standardize the design and thus ensure the safe dimensioning of components. 

Various factors are taken into account in the guidelines, such as the material, the external load or the notch shape. Since crack initiation generally always starts from the component surface and the local properties present here can accelerate or delay this, the surface and subsurface properties are of particular importance in the strength calculation. Nevertheless, it is still difficult to take into account manufacturing processes such as mechanical surface treatment in the guidelines, even though their positive effect has been known and scientifically proven for almost 100 years. 

The three guidelines mentioned take into account the surface and subsurface properties in varying degrees of detail and accuracy. Roughness is taken into account in all three guidelines. This also seems perfectly logical, as the surface roughness represents micro-notches from which cracks can originate. The hardness and the existing residual stresses are taken into account differently. The newer FVA guideline already uses these properties in the calculation. The more common frameworks of the FKM and DIN 743 summarize the hardness and residual stress in the so-called K_v-factor. If the designer wants to take these properties into account, he uses this correction factor. For example, if a component is to be deep rolled or shot peened, the K_v-factor is set to a value slightly above 1. The higher the value, the greater the expected effect of deep rolling or shot peening. The closer the value is to 1, the less influence is expected from machining. As the designer is responsible for the service life of the component, he will always choose this value rather conservatively and close to 1. The consequence of this is that, in purely mathematical terms, mechanical surface treatment can usually bring no advantages and is therefore not used. However, if resources are to be saved in the long term by using deep rolling, machine hammer peening or shot peening, then the predictive accuracy of the guidelines must be further increased. 

Ms. Günther and her colleagues addressed precisely this question in their study: How can the accuracy of strength verifications of deep-rolled notched components be evaluated? 

Investigations into differently notched test components made from 42CrMo4 + QT were presented. The test parts had three different notch shapes: unnotched, mildly notched and sharply notched. The diameter of the test specimens varied between 10 and 36 millimetres. Both small test specimens and real components were examined. For the service life assessment, tests were carried out under tensile-compression, rotating bending and torsion loads and a comparison was then made with the theoretically calculated predictions. 

Deep rolling of the notch radii was carried out using a single-roller mechanical rolling tool type EG5-1 with a 40M roller. The roll radius was designed to match the notch radius. The appropriate deep rolling forces and feed rates were determined in preliminary tests. The samples were processed at a contract manufacturer under series production conditions with consistent quality in order to minimize the scattering of the tests. 

The comparison with the calculated values from the guidelines can be found in the publication. However, the results show that deep rolling offers an enormous advantage, especially for notched samples under bending loads, and that the strength of the shafts can be almost doubled. The diagram shows the comparison between a mildly notched and a sharply notched shaft with and without deep rolling. The two loads, tension-compression and bending circulation, are shown.

It can be seen that the nominal stress amplitude decreases as the notch becomes sharper, meaning that the components can withstand less load. This applies to the tension-compression case as well as to the bending circulation load. Deep rolling can increase the nominal stress amplitude in any case, whereby this effect increases again with a sharper notch geometry. In the most favorable case, deep rolling can increase the nominal stress amplitude by 94% with a sharp notch under bending circulation load, which corresponds to almost a doubling of the strength.

Deep rolling therefore has great potential for extending service life and therefore resource efficiency in the design of shafts. The study by Ms. Günther and her colleagues shows that we can also exploit this potential with the right calculation approaches.